Stability of Wilson’s functional equations with involutions

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• 作者：Jaeyoung Chung ; Prasanna K. Sahoo
• 关键词：39B82 ; d’Alembert’s functional equation ; involution ; stability ; Wilson’s functional equation
• 刊名：Aequationes Mathematicae
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：89
• 期：3
• 页码：749-763
• 全文大小：508 KB
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• 作者单位：Jaeyoung Chung (1)
  Prasanna K. Sahoo (2)
  
  1. Department of Mathematics, Kunsan National University, Kunsan, 573-701, Republic of Korea
  2. Department of Mathematics, University of Louisville, Louisville, KY, 40292, USA
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Combinatorics
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8903

文摘

Let S be a commutative semigroup, \({\mathbb{C}}\) the set of complex numbers, \({\mathbb{R}^+}\) the set of nonnegative real numbers, \({f, g : S \to \mathbb{C}\, \, {\rm and} \, \, \sigma : S \to S}\) an involution. In this article, we consider the stability of the Wilson’s functional equations with involution, namely \({f(x + y) + f(x + \sigma y) = 2f(x)g(y)}\) and \({f(x + y) + f(x + \sigma y) = 2g(x)f(y)}\) for all \({x, y \in S}\) in the spirit of Badora and Ger (Functional equations—results and advances, pp 3-5, 2002). As consequences of our results, we obtain the superstability of functional equations studied by Chung et?al. (J Math Anal Appl 138:208-92, 1989), Chavez and Sahoo (Appl Math Lett 24:344-47, 2011) and Houston and Sahoo (Appl Math Lett 21:974-77, 2008).